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Question(s) from Search: IIT

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701

If  
then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent.

a) True

b) False

If  
then the two triangles with vertices (x1, y1), (x2, y2), (x3, y3), and (a1, b1), (a2, b2), (a3, b3) must be congruent.

a) True

b) False

IIT 1985
702

If  then

a)

b)

c)

d) f and g cannot be determined

If  then

a)

b)

c)

d) f and g cannot be determined

IIT 1998
703

A curve passes through  and slope at the point  is

. Find the equation of the curve and the area between the

curve and the X-axis in the fourth quadrant.

A curve passes through  and slope at the point  is

. Find the equation of the curve and the area between the

curve and the X-axis in the fourth quadrant.

IIT 2004
704

Find the integral solutions of the following system of inequality
 

a) Ø

b) x = 1

c) x = 2

d) x = 3

Find the integral solutions of the following system of inequality
 

a) Ø

b) x = 1

c) x = 2

d) x = 3

IIT 1979
705

Cosine of angle of intersection of curve y = 3x – 1lnx and y = xx – 1 is

Cosine of angle of intersection of curve y = 3x – 1lnx and y = xx – 1 is

IIT 2006
706

Let A =

 
AU1 =  , AU2 =  and AU3 =

 

a) −1

b) 0

c) 1

d) 3

Let A =

 
AU1 =  , AU2 =  and AU3 =

 

a) −1

b) 0

c) 1

d) 3

IIT 2006
707

If f : [1, ∞) → [2, ∞) is given by  then  equals

a)

b)

c)

d)

If f : [1, ∞) → [2, ∞) is given by  then  equals

a)

b)

c)

d)

IIT 2001
708

For the primitive differential equation
 

then  is

a) 3

b) 5

c) 1

d) 2

For the primitive differential equation
 

then  is

a) 3

b) 5

c) 1

d) 2

IIT 2005
709

Consider the system of linear equations
 
 
 
Find the value of θ for which the systems of equations have non-trivial solutions.

Consider the system of linear equations
 
 
 
Find the value of θ for which the systems of equations have non-trivial solutions.

IIT 1986
710

The set of all solutions of the equation

The set of all solutions of the equation

IIT 1997
711

Multiple choices with one or more than one correct answers
  then

a) x = f(y)

b) f(1) = 3

c) y increases with x for x < 1

d) f is a rational function of x

Multiple choices with one or more than one correct answers
  then

a) x = f(y)

b) f(1) = 3

c) y increases with x for x < 1

d) f is a rational function of x

IIT 1984
712

Given  and f(x) = cosx – x(x + 1). Find the range of f (A).

Given  and f(x) = cosx – x(x + 1). Find the range of f (A).

IIT 1980
713

Multiple choices

If the first and  term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then

a)

b)

c)

d)

Multiple choices

If the first and  term of an Arithmetic Progression, a Geometric Progression and a Harmonic Progression are equal and their nth term are a, b, c respectively then

a)

b)

c)

d)

IIT 1988
714

Show that the value of  wherever defined, never lies between  and 3.

Show that the value of  wherever defined, never lies between  and 3.

IIT 1992
715

Let  where A, B, C are real numbers. Prove that if f(n) is an integer whenever n is an integer, then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C all integers then f(n) is an integer whenever n is an integer.

Let  where A, B, C are real numbers. Prove that if f(n) is an integer whenever n is an integer, then the numbers 2A, A + B and C are all integers. Conversely prove that if the numbers 2A, A + B and C all integers then f(n) is an integer whenever n is an integer.

IIT 1998
716

Let  and  be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is  then
 is equal to

a) 1

b)

c)

d) None of these

Let  and  be three non-zero vectors such that c is a unit vector perpendicular to both the vectors a and b and the angle between the vectors a and b is  then
 is equal to

a) 1

b)

c)

d) None of these

IIT 1986
717

Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?

Does there exist a Geometric Progression containing 27, 8 and 12 as three of its terms? If it exists, how many such progressions are possible?

IIT 1982
718

The values of  lies in the interval .  .  .

The values of  lies in the interval .  .  .

IIT 1983
719

If  and  then (gof)(x) is equal to

If  and  then (gof)(x) is equal to

IIT 1996
720

If 0 < x < 1, then  is equal to

If 0 < x < 1, then  is equal to

IIT 2008
721

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

The sum of integers from 1 to 100 that are divisible by 2 or 5 is

IIT 1984
722

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

The minimum value of the expression  where  are real numbers satisfying  is

a) Positive

b) Zero

c) Negative

d) –3

IIT 1995
723

Using the relation , or otherwise prove that

a) True

b) False

Using the relation , or otherwise prove that

a) True

b) False

IIT 2003
724

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

If A > 0, B > 0 and A + B = , then the maximum value of tan A tanB is ……….

a)

b)

c)

d)

IIT 1993
725

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

Let  be non–coplanar unit vectors equally inclined to one another at an angle θ. If find p, q, r in terms of θ

IIT 1997

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